## Abstract

When the GMBACK solver is used in the Newton iterates, the iterates may be written either as inexact Newton iterates or as quasi-Newton iterates. In this paper present results which assure the local convergence of the iterates in the both settings.

## Authors

Emil Catinas

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

## Keywords

linear systems; Krylov solvers; GMBACK; backward error.

## Cite this paper as:

E. Catinas, * On the convergence of the Newton-GMBACK method.* 2007 International Conference on Engineering and Mathematics, Bilbabo, July 9-11, 2007, pp.11-14.

### References

see the expansion block below.

Not available yet.

## About this paper

##### Journal

##### Publisher Name

##### DOI

##### Print ISSN

##### Online ISSN

## MR

?

## ZBL

?

[1 E. Catinas, * Inexact perturbed Newton methods and applications to a class of Krylov solvers, * I. Optim. Theory, Appl. 108 (2001), 543-570.

[2] E. Catinas, * On the superlinear convergence of the successive approximations method, * J. Optim. Theory Appl., 113 (2002), 473-485.

[3] E. Catinas, *The inexact perturbed and quasi-Newton methods are equivalent models*, Math. Comp., 74 (2005), no. 249, pp. 291-301.

[4] R. S. Dembo, S.C. Eisenstat and T. Steihaug, * Inexact Newton methods, *SIAM, J. Numer. Anal. 19 (1982), 400-408.

[5] J. E. Dennis, Jr. and J. J. More, * A characterization of superlinear convergence and its application to quasi-Newton methods, * Math. Comp. 28 (1974), 549-560.

[6] E. M. Kasenally, *GMBACK: a generalised minimum backward error algorithm for nonsymmetric linear system, *SIAM J. Sci. Comput. 16 (1995), 698-719.

[7] E. M. Kasenally and V. Simoncini, * Analysis of a minimum perturbation algorithm for nonsymmetric linear systems, *SIAM J. Numer. Anal. 34 (1997), 48-66.

[8] B. Morini, *Convergence behaviour of inexact Newton methods, *Math. Comp. 68 (1999), 1605-1613.

[9] J. M. Ortega and W. C. Rheinboldt, *Iterative Solution of Nonlinear Equations in Several Variables, *Academic Press, New York, 1970.

[10] F. A. Potra, *On Q-order and R-order of convergence*, J. Optim. Theory Appl. 63 (1989), 415-431.

soon